Dales G., et al. - Introduction to Banach Algebras, Operators, and Harmonic Analysis (Cambridge, 2003).pdf - Algebra - Mathematics2014

This work has arisen from lecture courses given by the authors on impor-

tant topics within functional analysis. The authors, who are all leading re-

searchers, give introductions to their subjects at a level ideal for beginning

graduatestudents,aswellasothersinterestedinthesubject.Thecollectionhas

beencarefullyeditedtoformacoherentandaccessibleintroductiontocurrent

researchtopics.

The ﬁrst part of the book, by Professor Dales, introduces the general theory

ofBanachalgebras,whichservesasabackgroundtotheremainingmaterial.

DrWillisthenstudiesacentrallyimportantBanachalgebra,thegroupalgebraof

alocallycompactgroup.TheremainingchaptersaredevotedtoBanachalgebras

ofoperatorsonBanachspaces:ProfessorEschmeiergivesallthebackground

fortheexcitingtopicofinvariantsubspacesofoperators,anddiscussessome

key open problems; Dr Laursen and Professor Aiena discuss local spectral

theoryforoperators,leadingintoFredholmtheory.

LONDON MATHEMATICAL SOCIETY STUDENT TEXTS

Managing editor: ProfessorW.Bruce,DepartmentofMathematics

UniversityofLiverpool,UnitedKingdom

3 Local ﬁelds, J.W.S.CASSELS

4 An introduction to twister theory, second edition ,S.A.HUGGET&K.P.TOD

5 Introduction to general relativity ,L.P.HUGHSTON&K.P.TOD

7 The theory of evolution and dynamical systems ,J.HOFBAUER&K.SIGMUND

8 Summing and nuclear norms in Banach space theory ,G.J.O.JAMESON

9 Automorphisms of surfaces after Nielson and Thurston ,A.CASSON&S.BLEILER

11 Spacetime and singularities ,G.NABER

12 Undergraduate algebraic geometry ,M.REID

13 An Introduction to Hankel operators ,J.R.PARTINGTON

15 Presentations of groups, second edition ,D.L.JOHNSON

17 Aspects of quantum ﬁeld theory in curved spacetime ,S.A.FULLING

18 Braids and coverings: Selected topics ,V.LUNDSGAARDHANSEN

19 Steps in commutative algebra ,R.Y.SHARP

20 Communication theory ,C.M.GOLDIE&R.G.E.PINCH

21 Representations of ﬁnite groups of Lie type ,P.DIGNE&J.MICHEL

22 Designs, graphs, codes, and their links ,P.J.CAMERON&J.H.VANLINT

23 Complex algebraic curves ,F.KIRWAN

24 Lectures on elliptic curves ,J.W.S.CASSELS

25 Hyperbolic geometry ,B.IVERSEN

26 An introduction to the theory of L-functions and Eisenstein series ,H,HIDA

27 Hilbert space: Compact operators and the trace theorem ,J.R.RETHERFORD

28 Potential theory in the complex lane ,T.RANSFORD

29 Undergraduate cummutative algebra ,M.REID

31 The Laplacian on a Rlemannian manifold ,S.ROSENBERG

32 Lectures on Lie groups and Lie algebras ,R.CARTER,G.SEGAL&J.MACDONALD

33 A primer of algebraic D-modules ,S.C.COUTINHO

34 Complex algebraic surfaces ,A.BEAUVILLE

35 Young tableaux ,W.FULTON

37 A mathematical introduction to wavelets ,P.WOJTASZCZYK

38 Harmonic maps, loop groups and integrable systems ,M.GUEST

39 Set theory for the working mathematician ,K.CIESIELSKI

40 Ergodic theory and dynamical systems ,M.POLLICOTT&M.YURI

41 The algorithmic resoution of diophantine equations ,N.P.SMART

42 Equlibrium states in ergodic theory ,G.KELLER

43 Fourier analysis on ﬁnite groups and applications ,A.TERRAS

44 Classical invariant theory ,P.J.OLVER

45 Purmutation groups ,P.J.CAMERON

46 Rlemann surfaces: A primer ,A.BEARDON

47 Introductory lectures on rings and modules ,J.BEACHY

48 Set theory ,A.HAJNAL&P.HAMBURGER

49 An introduction to K-theory for C ∗ -algebras ,M.RØRDAM,F.LARSEN&

N.JLAUSTSEN

50 A brief guide to algebraic number theory ,H.P.F.SWINNERTON-DYER

51 Steps in commutative algebra ,R.Y.SHARP

52 Finite Markov chains and algorithmic applications ,O.HAGGSTROM

53 The prime number theorem ,G.J.O.JAMESON

54 Topics in graph automorphisms and reconstruction ,J.LAURI&R.SCAPELLATO

55 Elementary number theory, group theory and Ramanujan graphs ,P.SARNAK,

G.DAVIDOFF&A.VALETTE

56 Logic, induction and sets ,T.FORSTER

INTRODUCTIONTOBANACH

ALGEBRAS,OPERATORS,AND

HARMONICANALYSIS

H. GARTH DALES

University of Leeds, UK

PIETROAIENA

Universita degli Studi, Palermo, Italy

JORGESCHMEIER

Universitat des Saarlandes, Saarbrucken

KJELDLAURSEN

University of Copenhagen, Denmark

GEORGEA.WILLIS

University of Newcastle, New South Wales, Australia

Cambridge, New York, Melbourne, Madrid, Cape Town, Singapore, São Paulo

Cambridge University Press

The Edinburgh Building, Cambridge , United Kingdom

Published in the United States of America by Cambridge University Press, New York

www.cambridge.org

Information on this title: www.cambridge.org/9780521828932

This book is in copyright. Subject to statutory exception and to the provision of

relevant collective licensing agreements, no reproduction of any part may take place

without the written permission of Cambridge University Press.

First published in print format

2003

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s for external or third-party internet websites referred to in this book, and does not

guarantee that any content on such websites is, or will remain, accurate or appropriate.

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